I take my shoes off at the door and enter a living room where everything is coloured blood red: the carpet, the sofa, the cushions, the cabinets, the paintings on the wall. At the far end, a pitch-black corridor leads past a trail of "spilt" red paint, where a sudden spotlight shines on a wonky washbasin and a gushing stream of water – red water.

Cildo Meireles' Red Shift is playful, somewhat sinister and was once briefly loaned to the Tate Modern in London. But what does it all mean? I have no idea. I contemplate it for a moment as I go back outside, blinking in the bright Brazilian sunshine, surrounded again by subtropical foliage and flowers. Then I unfold my map again to pick the next experience.

Cildo Meireles' Red Shift at Inhotim.

This is Inhotim, a giant open-air art gallery set amid 500,000 acres of botanical gardens in south-east Brazil, two hours from World Cup city Belo Horizonte. Its grounds are dotted with sculptures, art pavilions and over 4,000 plant species. On arrival, you are given a map that shows the attractions, spread far and wide, and then you pick your route. You can either get around on foot or, for a about £5 per person, in a chauffered golf cart. Either way, you'll never see it all; some art enthusiasts buy multi-day passes.

The Centro de Arte Contemporânea Inhotim was founded by mining magnate Bernardo Paz and designed by the late landscape artist Roberto Burle Marx, Paz′s friend. It opened to the public in 2006. The collection is a mix of works from Brazilian and international artists, including Olafur Eliasson, Doug Aitken, Vik Muniz, Anish Kapoor and Adriana Varejão. Many of the pavilions are works of art in themselves – one resembles an igloo, another a floating block of concrete. And the exhibits range from the mesmerising (a labyrinth of mirrors camouflaged into the forest so well that saucer-sized butterflies keep bashing into the glass) to the absurd (a row of garden hoes).

Photograph: Marcelo Coelho

Much of it is interactive, too. On a hillside clearing you can spin Olafur Eliasson's kaleidoscopic telescope around to look at the trees. In another room, there's a pool of water in the centre, where a sign I presume to be a caution turns out to be an invitation to swim. There are also a variety of restaurants, from hotdog kiosks to a chic bistro and a pay-per-kilo Brazilian buffet.

Inhotim has been called an art zoo, a cultural Disneyland, and, tenuously, a Jurassic Park for contemporary art. It's also a money pit. Paz employs over 1,000 staff and says keeping it open costs him R$2m (around £500,000) every month. Ticket sales (priced £5 to £8 per head) make minimal returns – especially as there's free entry on Tuesdays, a deliberate move to ensure it stays accessible to locals and students.

The long-term plan is to turn it into a destination in itself, with an 80-room luxury hotel and spa in the pipeline and more resorts planned. New pavilions are currently under construction and the park seems to be realising only a fraction of its potential. (Of those 500,000 acres, only 110 make up the current network of trails.) Paz, having sold his mining company to a Chinese investor in 2010 for $1.2bn, should have the funds to prop it up for a good while yet. And even if that remains an uphill battle, as investments go, it has much greater prospects than a $300m football stadium in the middle of the Amazon.

Galeria True Rouge at Inhotim. Photograph: Alamy

• Inhotim (+55 31 3571 9700, inhotim.org.br). Admission R$20-R$30 (£5–£7.50), closed on Monday, free on Tuesday. Buses from Belo Horizonte bus station (60km away) depart at 8.15am and return at 4.30pm or 5pm at the weekend with Saritur (R$23/£6 each way). Throughout the World Cup, until 13 July, there will be an additional pick-up from Hotel Mercure Lourdes, Avenida Do Contorno 7315, if booked online at least 12 hours ahead. Real World Holidays has a 10-day trip to São Paulo, Belo Horizonte and Rio for £1,295pp, including hotels, transport, internal (but not international) flights, guides and tours. Flights from London to Rio via Lisbon with TAP Portugual cost from £650 return including taxes